Your sunstar did not die, it is taking a short rest. Here are instructions for it, but think you have to keep yours indoors in your area in winter.
http://www.ubcbotanicalgarden.org/forums/showthread.php?t=6638

Darlene

Your plant is Ornithogalum dubium. It is native to South Africa and is NOT hardy for you. It is most often sold as a flowering houseplant. A Google search under the botanical name will turn up various sites listing care instructions but most indicate that it is very difficult to encourage this plant to return after dormancy, let alone rebloom. It may be best treated as if it were a very long lasting cut flower :-)